
Here, the three matrix symmetries correspond to \(\beta =1,2\)  and 4, respectively, also see [1]}. Dyson [2]} also found that the system of independent one-dimensional Brownian motions with the condition that they never collide with each other satisfy (REF ), also see [3]} and references therein. Such stochastic processes satisfying (REF ) or (REF ) are called Dyson's Brownian motion. In this paper, we refer to Dyson's Brownian motion as a solution of (REF ). The solutions of SDEs (REF ) and (REF ) with general \(\beta >0\)  are studied. Rogers and Shi [4]} proved that if \(\beta \ge 1\) , these solutions never collide with each other nor explode almost surely. Cépa and Lépingle [5]} proved the existence of unique strong solution for \(\beta >0\)  with a reflecting boundary condition.
